Okay, I'm back from lunch with the (hardcover!) booklet from the CD collection, "The Remains of Tom Lehrer" (©2000 Warner Bros. Records Inc. & Rhino Entertainment Company). Here are some quotes:

From a Q&A on page 28:
Q: How come the song you wrote for the Rock Hudson movie '"A Gathering of Eagles" ("The SAC Song") was never published or recorded?
A: It was writtenn to illustrate a particular point in the plot of the movie and is not clever enough to be of interest out of context.
Q: Your record "That Was The Year That Was" included nine songs from the TV show TW3 ("That Was The Week That Was"). Were there other songs from that show that you didn't include but that exist somewhere?
A: There were a few others, but they weren't interesting enough to record. (Trust me.) Some kinescopes or audiotapes of the show no doubt exist somewhere, but I doubt that they include any of those other songs.
Q: Do you have any unreleased songs that may someday see the light of day?
A: I have none that I think are worth recording [other than the ones which were added for this box set], but—who knows?—some day my standards may decline.

From a bio on page 20:
"He had done a few television shows along the way, mostly in Australia and Europe...." This is the only mention of personal appearances on TV. He never appeared on TW3; the regulars on the show sang his songs.

In 1971 and 1972, Lehrer was asked to contribute songs for the public TV children's show "The Electric Company". His recordings were used as soundtracks for animation: "In 'O-U', for example, I was the voice of a dog." (page 42). The CD collection includes five of those songs but there's no mention of the total number of pieces that he created for this program.

So there ya go. We can only hope Tom Lehrer lowers his "standards" and records these songs during his lifetime, or that at the very least he hasn't destroyed them. Just because they don't interest HIM doesn't mean the rest of us have forgotten them... obviously!